I am working on a project that is using a custom 1:1 aspect ratio display, or a series of them. I need to produce some "mock up" content on the display, is there any way to export a 1:1 DVD to play on the displays HDMI in?

As Jim says, you may need to find a player like my IO-Data (way old and no longer available) that plays Windows Media files from a CD or DVD or USB. But mine is Component video, not HDMI.

Or, get a small PC with HDMI output from the video card to play your video. Maybe even a laptop.

On the other hand, what would the 1:1 player do with a 16:9 or 4:3 image? If it center cuts it, then just drop your footage on to a 16:9 or 4:3 sequence with black bars on the side and see how it looks.